Concept Architecture
Concept
Theoretically, the Kaplan-Meier Method is a non-parametric statistical method for estimating the survival function from time-to-event data in the presence of right censoring. It is based on the product-limit approach developed by Kaplan and Meier and provides an empirical estimate of survival without assuming any underlying probability distribution. In health economics, the Kaplan-Meier method is the standard approach for analysing survival outcomes from clinical studies and provides the empirical basis for subsequent survival modelling and economic evaluation.
Mathematically, the Kaplan-Meier method estimates survival by multiplying the conditional probabilities of surviving each observed event time. The resulting survival function is a step function that changes only when an event occurs, while censored observations contribute to the number at risk but do not directly reduce the estimated survival probability. Under the assumption of independent censoring, the method provides a consistent estimate of the true survival function.
In practice, the Kaplan-Meier method is implemented using statistical software to estimate overall survival, progression-free survival and disease-free survival. It is routinely used to compare treatment groups, estimate median survival, generate Kaplan-Meier curves and provide the empirical benchmark against which parametric survival models are selected for long-term extrapolation in health economic evaluations.
Purpose
Used to estimate survival probabilities from censored time-to-event data, compare treatment groups and provide empirical survival estimates for survival modelling and health economic evaluation.
Mathematical Formulae
Primary Formula
?(t) = ???�? (1 ? d? / n?)
where:
- ?(t) = estimated survival probability
- d? = number of events at time t?
- n? = number at risk immediately before time t?
Supporting Formulae
Conditional survival probability:
p? = 1 ? d? / n?
Median survival:
?(t?.?) � 0.5
Related Mathematical Methods
- Kaplan-Meier estimator
- Kaplan-Meier curve
- Log-rank test
- Cox proportional hazards model
- Nelson-Aalen estimator
- Parametric survival modelling
- Survival analysis
Example
A five-year clinical trial evaluates overall survival in patients receiving a new oncology treatment. The Kaplan-Meier method is used to estimate survival probabilities at each observed death while accounting for patients lost to follow-up. The resulting survival estimates are used to compare treatments and to evaluate the fit of alternative parametric survival models for lifetime cost-effectiveness analysis.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =1-(C2/B2) | Calculate conditional survival probability at each event time. |
| PRODUCT | =PRODUCT(E$2:E2) | Calculate cumulative Kaplan-Meier survival estimates. |
| COUNTIFS | =COUNTIFS(TimeRange,">="&A2) | Calculate the number of patients at risk immediately before each event time. |
| MATCH | =MATCH(0.5,F2:F100,-1) | Identify the estimated median survival time from the Kaplan-Meier survival function. |
VBA (Optional)
Automate Kaplan-Meier survival estimation, generate survival tables and produce publication-ready Kaplan-Meier analyses from patient-level datasets.
Sources
- Kaplan EL, Meier P. Nonparametric Estimation from Incomplete Observations.
- Klein JP, Moeschberger ML. Survival Analysis: Techniques for Censored and Truncated Data.
- Collett D. Modelling Survival Data in Medical Research.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
NICE DSU Technical Support Document 14: Survival analysis for economic evaluations alongside clinical trials – extrapolation with patient-level data — Nicholas R. Latimer, TSD 14 ed., 2013 (NICE Decision Support Unit (University of Sheffield))
The reference guidance on survival analysis for economic evaluation: fitting standard parametric models (exponential, Weibull, Gompertz, log-logistic, log-normal) to censored trial data and extrapolating to estimate lifetime survival benefit, with a process guide for model selection and justification.
Frequently Asked Questions (6)
What is the Kaplan-Meier method?
The overall approach of estimating and comparing survival functions using the Kaplan-Meier estimator, accounting for censored observations in time-to-event data.
Source: Kaplan & Meier 1958
What can the Kaplan-Meier method not do?
The Kaplan-Meier method summarises observed survival and compares groups, but it stays within the data it is given and cannot project beyond the last follow-up, so it yields no estimate of long-term or mean survival once follow-up ends. Nor can it adjust for several covariates at once or model how risk depends on patient characteristics, which requires a regression approach such as the Cox model. It describes what was observed rather than explaining or extending it. Its role is descriptive. Collett (2015) notes these limits.
Source: Collett 2015
What does the Kaplan-Meier method involve?
The Kaplan-Meier method involves estimating the survival function from censored data using the product-limit estimator, presenting it as a step-function survival curve, reading quantities such as survival probabilities and median survival from it, and comparing survival between groups, often using the log-rank test. It accounts for censoring by keeping censored individuals at risk until their censoring time. Together these steps make up the standard non-parametric analysis of survival data, from estimation through display to group comparison.
Source: Kaplan & Meier 1958
How does the Kaplan-Meier method compare groups?
The Kaplan-Meier method compares groups by estimating separate survival curves for each and comparing them, visually and formally. The log-rank test is commonly used to test whether the survival distributions differ, comparing observed and expected events across groups over time. A lower curve indicates worse survival. This allows the survival experience of different groups, such as treatment arms, to be compared non-parametrically, showing whether and how their survival differs, though the comparison does not by itself quantify the effect as the Cox model does.
Source: Collett 2015
When is the Kaplan-Meier method used?
The Kaplan-Meier method is used to describe and compare survival in time-to-event data with censoring, such as survival or time to progression in clinical studies, when a non-parametric estimate that makes no distributional assumption is wanted. It is the standard first step in survival analysis, providing survival curves and group comparisons. For modelling covariate effects or extrapolating long-term survival, it is complemented by regression models such as the Cox model and by parametric distributions, since the method itself does not provide these.
Source: Kaplan & Meier 1958
What are the limitations of the Kaplan-Meier method?
The Kaplan-Meier method is limited by giving unreliable estimates at later times with few at risk, by not extrapolating beyond the observed follow-up, and by not modelling covariate effects, which require regression. Its group comparison via the log-rank test does not quantify the size of the effect, and it assumes non-informative censoring. These limitations mean the method is used for describing and comparing observed survival, while parametric models and regression are used for extrapolation and for estimating covariate effects.
Source: Collett 2015
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 21 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/kaplan-meier-method
- Term code
- HE-EM-SM-039
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